Growth and order of automorphisms of free groups and free Burnside groups

Coulon, Rémi¹ ; Hilion, Arnaud²

¹ Institut de Recherche Mathématique de Rennes - UMR 6625, CNRS - Université de Rennes 1, Campus de Beaulieu, bâtiments 22 et 23, 263 avenue du Général Leclerc, CS 74205, 35042 Rennes Cedex, France
² I2M UMR 7373 - Centre de Mathématiques et Informatique, Aix Marseille Université, CNRS, Centrale Marseille, I2M, Marseille, France, Technopôle Château-Gombert, 39, rue F Joliot Curie, 13453 Marseille 13, France

Geometry & topology, Tome 21 (2017) no. 4, pp. 1969-2014.

Résumé

We prove that an outer automorphism of the free group is exponentially growing if and only if it induces an outer automorphism of infinite order of free Burnside groups with sufficiently large odd exponent.

Détail

DOI : 10.2140/gt.2017.21.1969

Classification : 20E05, 20E36, 20F28, 20F50, 20F65, 68R15
Keywords: automorphism groups, free groups, Burnside groups, growth of automorphisms, train-track theory

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